Persistent random walk on a one-dimensional lattice with random asymmetric transmittances.

We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance t (t;{'} not equalt) for photons moving to the right (left) direction. Transmittances at different sites are assumed independent, distributed according to a given probability density F(t,t;{'}) . We use the effective medium approximation and identify two classes of F(t,t;{'}) which lead to the normal diffusion of photons. Monte Carlo simulations confirm our predictions. We mention that the metamaterial introduced by Fedetov [Nano Lett. 7, 1996 (2007)] can be used to realize a lattice of random asymmetric transmittances.